The process of optimizing output data is an important process for any entity. For instance, an entity such as a business entity, organization, or the like would like to maximize the revenue that it earns on a product line, the profit that it earns on a product line, the number of products that it sells, etc. Alternatively, the entity may want to minimize the costs associated with selling products on a product line, minimize the number of employees working in a department of the entity, minimize the overhead associated with a particular product line, etc. In order to achieve each of these objectives, the entity may design one or more optimization functions.
A maximizing or minimizing objective function is subject to one or more constraints. For instance, the constraints imposed on the goal of maximizing revenue on a product line may be a limited budget, a limited number of sales channels, a limited time period for selling the product, etc.
An objective function depends on unknown variables whose values need to be determined in order to solve an optimization problem. In general, an optimization problem is an objective function that is subject to one or more input constraints. One type of an optimization problem is a binary programming (BP) problem. A BP problem is an instance where unknown variables of an objective function can take values of either 0 or 1. In general, BP problems are part of the class of IP (integer programming) problems. An IP problem is an instance where unknown variables of an optimization problem take integer values. When the population dataset is sufficiently large, the BP problem is an ELSBP (extra-large scale binary programming) problem which is part of the class of ELSIP (extra-large scale integer programming) problems.
In general, IP problems are NP-hard (non-deterministic polynomial-time hard) problems. In computational complexity theory, these problems are at least as hard as the hardest problems in NP. A problem ‘H’ is NP-hard if and only if there is an NP-complete problem ‘L’ that is polynomial time Turing-reducible to ‘H.’ A problem ‘L’ is NP-complete if it has two properties: (1) it is in the set of NP (nondeterministic polynomial time) problems, i.e., any given solution to ‘L’ can be verified quickly (in polynomial time); and (2) it is also in the set of NP-hard problems, i.e., any NP problem can be converted into ‘L’ by a transformation of the inputs in polynomial time.
Current optimization systems do not have the ability to efficiently optimize output data associated with a population greater than 50,000 objects. Therefore, there is a need for a system that has the ability to optimize output data associated with populations greater or much greater than 50,000, such as a population of 10,000,000 or greater.
Current optimization systems or solver systems do not have the capacity to produce output data in a short period of time when the size or volume of the population becomes too large. Therefore, there is a need for a system that runs faster and has the ability to produce accurate output data associated with a large population in a short period of time.
Current optimization systems are also cumbersome to use. Therefore, there is a need for a system that is easier to use, i.e., more user-friendly. For instance, there is a need for a system that allows a user to more easily define or modify an optimization problem, allows a user to change input constraints upon which the optimization problem is solved, allows a user to define a range for each input constraint, allows a user to view output data from a plurality of output scenarios, etc.